First slide

Simple hormonic motion

Question

A particle is vibrating in SHM with an amplitude of 4cm. At what displacement from the equilibrium position it has half potential and half kinetic

Easy

A

1cm
B

$\large \sqrt 2$ cm
C

2 cm
D

$\large 2\sqrt 2 \,cm$

Solution

$\large A\, = \,4cm;\,\,K.E\, = \,P.E$
$\large \frac{1}{2}m{\omega ^2}\left( {{A^2} - {y^2}} \right)\, = \,\frac{1}{2}m{\omega ^2}{y^2}$
$\large {A^2} - {y^2}\, = \,{y^2} \Rightarrow \,{A^2}\, = \,2{y^2}$
$\large y\, = \,\frac{A}{{\sqrt 2 }}\, = \,\frac{4}{{\sqrt 2 }} = \,2\sqrt 2 \,cm$

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